2015/08/12 by A. Mironov, A. Morozov, An. Morozov +1
Physics and Astronomy · Mathematics · #hep-th #math.GT #math.QA
paper · pdf · doi:10.1142/s0217751x15501699
published as Int. J. Mod. Phys. A 30 (2015) 1550169 · 25 pages
arxiv created 2015/08/12 · arxiv updated 2015/09/22
This paper starts a systematic description of colored knot polynomials, beginning from the first non-(anti)symmetric representation R=[2,1]. The project involves several steps: (i) parametrization of big families of knots a la arXiv:1506.00339, (ii) evaluating Racah/mixing matrices for various numbers of strands in various representations a la arXiv:1112.2654, (iii) tabulating and collecting the results at www.knotebook.org. In this paper we discuss only representation R=[2,1] and construct all necessary ingredients that allow one to evaluate knot/links represented by three strand closed parallel braids with inserted double-fat fingers. In particular, it is used to evaluate knots from a 7-parametric family: this family contains over 80% of knots with up to 10 intersections, but does not include mutants.